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CBSE Class 12-science Answered

solve integral fraction numerator x squared plus cos squared x over denominator 1 plus x squared end fraction cos e c squared x d x
Asked by Eng.surinder.singh | 26 Jan, 2019, 10:19: AM
answered-by-expert Expert Answer
begin mathsize 12px style I space equals space integral fraction numerator x squared plus cos squared x over denominator x squared plus 1 end fraction cos e c squared x space d x space equals space integral fraction numerator x squared cos e c squared x over denominator x squared plus 1 end fraction d x space plus space integral fraction numerator c o t squared x over denominator x squared plus 1 end fraction d x
I space equals space integral fraction numerator open parentheses x squared plus 1 minus 1 close parentheses begin display style cos end style begin display style e end style begin display style begin display style c end style squared end style begin display style x end style over denominator x squared plus 1 end fraction d x space plus space integral fraction numerator begin display style c o t squared x end style over denominator begin display style x squared plus 1 end style end fraction d x space space equals space integral cos e c squared x space d x space minus integral fraction numerator cos begin display style e end style begin display style begin display style c end style squared end style begin display style x end style over denominator x squared plus 1 end fraction d x space plus space integral fraction numerator begin display style c o t squared x end style over denominator begin display style x squared plus 1 end style end fraction d x
B y space u sin g space t h e space i d e n t i t y comma space space cos e c squared x space equals space 1 plus c o t squared x
I space equals space integral cos e c squared x space d x space minus integral fraction numerator d x over denominator x squared plus 1 end fraction space equals space minus c o t space left parenthesis x right parenthesis space minus space tan to the power of negative 1 end exponent x space plus space C end style
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